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Homemethods of evaluating improper integrals

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# methods of evaluating improper integrals

There are some general methods of evaluating improper integrals in such cases when one cannot directly use the antiderivative of the integrand. Which method is suitable in a certain instance, is dependent on the kind of the integral.

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Laplace transform. If the integrand has, as above, a parametre in a suitable place, the Laplace transform of the integrand with respect to this parametre is often simpler to integrate and the new improper integral to evaluate; thereafter one simply transforms inversely. Examples: f, g, h, i, j.

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Cauchy residue theorem. The integral may be obtained as limit of a contour integral in the complex plane. Examples: k, l, m, n.

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Expanding the integrand to series. Example: o.

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Changing variable in an improper integral sometimes may recur it to a known improper integral. Examples: p, q, r.

## Mathematics Subject Classification

40A10*no label found*

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